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   "source": [
    "Boolean values most often arise from comparison operators. Python includes a variety of operators that compare values. For example, `3` is larger than `1 + 1`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 1,
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   "source": [
    "3 > 1 + 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The value `True` indicates that the comparison is valid; Python has confirmed this simple fact about the relationship between `3` and `1+1`. The full set of common comparison operators are listed below.\n",
    "\n",
    "| Comparison         | Operator | True example | False Example |\n",
    "|--------------------|----------|--------------|---------------|\n",
    "| Less than          | <        | 2 < 3        | 2 < 2         |\n",
    "| Greater than       | >        | 3>2          | 3>3           |\n",
    "| Less than or equal | <=       | 2 <= 2       | 3 <= 2        |\n",
    "| Greater or equal   | >=       | 3 >= 3       | 2 >= 3        |\n",
    "| Equal              | ==       | 3 == 3       | 3 == 2        |\n",
    "| Not equal          | !=       | 3 != 2       | 2 != 2        |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An expression can contain multiple comparisons, and they all must hold in order for the whole expression to be `True`. For example, we can express that `1+1` is between `1` and `3` using the following expression."
   ]
  },
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   "cell_type": "code",
   "execution_count": 2,
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      "text/plain": [
       "True"
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     "execution_count": 2,
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   ],
   "source": [
    "1 < 1 + 1 < 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The average of two numbers is always between the smaller number and the larger number. We express this relationship for the numbers `x` and `y` below. You can try different values of `x` and `y` to confirm this relationship."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 12\n",
    "y = 5\n",
    "min(x, y) <= (x+y)/2 <= max(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Strings can also be compared, and their order is alphabetical. A shorter string is less than a longer string that begins with the shorter string."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"Dog\" > \"Catastrophe\" > \"Cat\""
   ]
  }
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